In recent years, in response to the escalating demands of the state regarding data security and privacy safeguarding, federated learning has emerged as a prominent research focus. Nevertheless, when dealing with heterogeneous datasets, federated learning suffers from a comparatively low accuracy level. Moreover, the model-sharing mechanism between clients and servers invariably imposes additional burdens on the overall system. In light of these challenges, this paper puts forward a clustered federated learning algorithm, namely CLF-GA. Firstly, a clustered federated learning approach predicated on gradient partitioning has been meticulously devised. During the model training process of clustered federated learning, parties with the same model training gradients should be grouped into one cluster. Gradients calculated from different models of clients are periodically accumulated and clustered, and clients showing similarity in gradient information during model updates are grouped together. Furthermore, a client cluster selection strategy has also been implemented. The server dynamically selects the number of clusters and the corresponding clusters participating in the global federated learning training according to the training status of each cluster. This enables underperforming clusters to secure more training prospects, thereby augmenting performance while concurrently curtailing system overhead. Experimental results show that our method not only reduces communication overhead but also outperforms advanced clustered federated learning methods in terms of training accuracy.